Abstract
This chapter looks in detail at a number of case studies from across the natural sciences, with the goal of identifying recurring strategies of model-building. Examples discussed range from target-oriented modeling in population biology (Lotka-Volterra model of predator–prey systems) to phenomenological models in physics (Ginzburg-Landau model of superconductivity) , which are often contrasted with causal-microscopic models (BCS model of superconductivity). Special attention is given to the constructive character of quantum many-body models, such as the BCS model or the Hubbard model of strongly correlated electrons. Against the view, defended by Nancy Cartwright, that many-body models must always be assessed in specific empirical contexts and that individual terms of a quantum Hamiltonian should never be ‘reified’, it is argued that not only is such a ‘separating out’ of individual terms typically unproblematic, but it often contributes to the intelligibility of the target system or phenomenon. The final part of the chapter discusses whether model-building necessarily involves trade-offs between different theoretical desiderata (such as generality and precision), and whether the existence of trade-offs can serve as a demarcation criterion between different scientific disciplines, notably biology and physics.
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Notes
- 1.
I am borrowing this way of contrasting phenomenological and mechanism-based models from [29, p. 427].
- 2.
See [30] for further discussion of the London model.
- 3.
This discussion follows [31, p. 248f.].
- 4.
There has been considerable debate about whether the case of superconductivity supports Cartwright’s claims, or whether it can be accommodated by theory-driven accounts of modeling. (For a defence of the latter claim, see [33].) At the same time, as Cartwright points out in a joint paper with Mauricio Suárez, the position she and her collaborators defend has sometimes been misinterpreted as an outright rejection of any constraining role of theory, when in fact it only asserts ‘that theories function as tools, not as sets of models already adequate to account for the startling phenomena that reveal their power’ [32, p. 66].
- 5.
For an insightful discussion of how the notion of ‘electron pairing’ developed over time, see [28, pp. 140–145].
- 6.
Because of the presence of parameters in the model that have not been derived from ‘first principles’, the BCS model is sometimes classified as 'phenomenological' by physicists: ‘However, [the BCS theory] must be considered as a phenomenological theory with respect to the use of an “effective potential” which describes the Coulomb and phonon-induced interactions between the electrons in a model.’ [34, p. 79].
- 7.
Regarding the notion of ‘mathematical formalisms’, and their ubiquity across the sciences, see [37].
- 8.
Further examples from other disciplines, including theoretical chemistry and traffic flow theory, will be discussed in Chap. 4.
- 9.
- 10.
My presentation in this paragraph mainly follows [20, pp. 1075–1079].
- 11.
Spelling out exactly how biological and physical ‘laws’ contrast with respect to universality, nomic force, or scope lies beyond the scope of this chapter. For a review of the debate about biological laws, see [35].
- 12.
Quoted after [22, p. 285].
- 13.
Contemporary climate models do well on this score and in a variety of other respects, such as robustness, variety of independent sources of evidence, and fit between observations and predictions (as well as retrodictions); indeed, as Elizabeth Lloyd has emphasized, ‘climate models are supported empirically in several ways that receive little explicit attention’ [36, p. 228].
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Gelfert, A. (2016). Strategies and Trade-Offs in Model-Building. In: How to Do Science with Models. SpringerBriefs in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-27954-1_3
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